Analysis of Linear Elastic Fracture Mechanics for Cracked Functionally Graded Composite Plate by Enhanced Local Enriched Consecutive-interpolation Elements - Dinh Duc, Nguyen; Nguyen, Dinh Du; Bui, Quoc Tinh (VNU Journal of Science: Mathematics - Physics; Vol 37 No 1, 2021)
This paper reports the application of consecutive-interpolation procedure into four-node quadrilateral elements for analysis of two-dimensional cracked solids made of functionally graded composite plate. Compared to standard finite element method, the recent developed consecutive-interpolation has been shown to possess many desirable features, such as higher accuracy and smooth nodal gradients it still satisfies the Kronecker-delta property and keeps the total number of degrees of freedom unchanged. The discontinuity in displacement fields along the crack faces and stress singularity around the crack tips are mathematically modeled using enrichment functions. The Heaviside function is employed to describe displacement jump, while four branch functions being developed from asymptotic stress fields are taken as basis functions to capture singularities. The interesting characteristic of functionall graded composite plate is the spatial variation of material properties which are intentionally designed to be served for particular purposes. Such variation has to be taken into account during the computation of Stress Intensity Factors (SIFs). Performance of the proposed approach is demonstrated and verified through various numerical examples, in which SIFs are compared with reference solutions derived from other methods available in literatures.